Using the given sample, test that the corresponding population has a Poisson distribution. x is the number of alpha particles per 7.5-s intervals observed by E. Rutherford and H. Geiger in one of their classical experiments in 1910, and ?(x) is the absolute frequency (= number of time periods during which exactly x particles were observed). Use ? = 5%.

X a a 0 57 7 139 1 203 8 45 2 3 383 525 9 10 27 10 4 5 532 408 11 12 4 2 6 273 13 0